Special relativity: interpretation and implications for space-time geometry

2009-06-05T12:47:57Z (GMT) by Homer Rahnejat
The paper commemorates the centenary of the special theory of relativity, which effectively sets the limit for the structure of space-time to that of the stationary system. The long lasting debate for definition of concepts of instantaneity and simultaneity was thus resolved by the declaration of constancy of speed of light in vacuo as a law of physics. All motions were thus bounded by the light cone and described by the properties of differential geometry, firmly anchored in the calculus of variations. The key contribution underpinning the theory was the resolution of the contradiction imposed by the Galilean transformation through physical explanation and the adoption of the Lorentzian transformation. This highlighted the relative nature of both space and time and the linkage of these to preserve the sanctity of the light cone. The resulting space-time geometry was then founded on the traditional calculus of variation with the addition of this transformation. This retains the time as an independent coordinate and its linkage to space in an explicit form. One implication of this approach has been the retention of the concept of infinitum for some physical quantities as a drawback for use of the Lorentzian transformation. The paper shows that this singular behaviour need not arise if the explicit linkage in space-time is abandoned in favour of the implicit inclusion of time as a link between the curved structure of space and the speed of light, thus restating the calculus of variation in line with special relativity. This points to a closed loop space-matter field, which may belie the fabric of the continuum. One implication of this interpretation is that a small variation in speed of light within the field would be required to dispense with the aforementioned singular nature of the Lorentzian boost, while still remaining within the spirit of special relativity.